Microhardness anisotropy in cubic Zro2

(1)

HAL Id: jpa-00245874

https://hal.archives-ouvertes.fr/jpa-00245874

Submitted on 1 Jan 1988

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Microhardness anisotropy in cubic Zro2

A. Pajares, F. Guiberteau, A. Dominguez-Rodriguez, A.H. Heuer

To cite this version:

A. Pajares, F. Guiberteau, A. Dominguez-Rodriguez, A.H. Heuer. Microhardness anisotropy in cubic Zro2. Revue de Physique Appliquée, Société française de physique / EDP, 1988, 23 (4), pp.719-719.

�10.1051/rphysap:01988002304071900�. �jpa-00245874�

(2)

719 MICROHARDNESS ANISOTROPY IN CUBIC ZrO2

_* **

A.PAJARES, F.GUIBERTEAU, A.DOMINGUEZ-RODRIGUEZ and A.H.HEUER.

Departamento ^de ^Fisica. F.Ciencias. Univ. Extremadura. 06071 BADAJOZ (SPAIN).

*Departamento ^de Optica. Facultad de Fisica. Aptdo 1065, 41080 SEVILLA (SPAIN).

**Department ^of Metallurgy and Materials Science, C.W.R.U., Cleveland, ^OHIO (U.S.A)

Revue Phys. Appl. ²³ (1988) ⁷¹⁹ ^AVRIL ^1988,

"he*hardness test is commonly ^used ^to determine the low temperature deformation characteristics of brittle compounds. ^With

this technique, several ^features ^can ^{be ob--} tained, mainly ^the ^fracture mechanism and

toughness, ^hardness anisotropy ^and slip _sys

tems.

In this work, the microhardness

on

(100) planes ⁱⁿ Y203-$tabilized ^cubic Zro2

single crystals has been studied using ^botn Knoop and Vickers indenters.

The Knoop ^hardness values(Hk) ^for dif

ferent loads and orientations

are

shovin in

fig.l. ^Crack free endentations are obtained for loads up to 2N and permit determination of the ratio of elastic modulus to hardness

(E/H), ^as ^follows /1/:

:b/dis the ratio of the diagonal lengths ⁱⁿ

the fully ^loaded state, ^{which is} ^defined by

the indenter geometry ând equal ^to 7.1; ^the ratio D’/d’ âfter unloading îs ^found equal to 8.3. ais

a

constant equal ^to 0 45 ^/1/.

Using ^this equation

^we

^find (E/H)1/2 ^{is in-}

dependent of orientation of the indenter di

agonal ^and equal to 4.7. The Knoop ^hardness

anisotropy(fig 1) is consistent with either

{100}011> ^or illll110> slip systems being

activated under the indenter. A similar

con

clusion was found in another Ytria - stabi-

lized cubic zirconia /2/.

With

a

Vickers indent and loads of 2N both radial and lateral cracks

^can

^occurs.

The lengths of the radial cracks which

are

along the indenter diagonals ^are ^different

for [100] ^and [110] directions, being short

er for [100]. The lateral cracks, ^which

^are

absent when the indenter diagonal ^is along

[110], allow the stress relaxation and pre- vent the radial cracks from propagating

^as

suggested by /3/.

The fracture toughness(Kc1) ^can ^be ob

tained from the len8ht of the radial crack, co, and the value of (E/H)1/2 ^determined

from the Knoop tests,

^as

^follows:

where

xr is

^a

^constant ^equal ^to ^0.016 ^/4/.

The reaYitionship P/co3/2 is shown in fiG.2

for the two orientations of the indenter di agonal. ^We find that Kc1 ^for (100) ^cracks

is 1.9 MPa ml/2, ^While Ioci ^for (110) ^ones

is 1.1 MPa ml/2.

The lower toughness ^for (100)compa.red

to (100)planes ^causes greater stress relief from the elastic / plastic incompatibility

during unloading., such that the incidence of lateral cracking ^is nearly reduced to ze

ro along [1101. This lower toughness along (110) ^can be correlated with the fact that the interplanar spacing normal to the (110) planes ^is larger than that normal to the

(100)planes, ^but

^a

^more microscopic expla-

tion must await future work.

REFERENCES

/1/ D.B.MARSHALL, T.NOMA and A.G.EVANS.

J.Am.Ceram.Soc. 65(1982),C-175.

/2/ J.LANKFORD. J.Mater.Sci. 21(1986),1981

/3/ R.F.COOK and D.H.ROACH. J.Am.Ceram.Soc (to ^be published).

/4/ C.R.ANSTINS, P.CHANTIKUL, B.R.LAWN and D.B.MARSHALL. J.Am.Ceram.Soc. 64(1981)

Fig.1. Knoop microhardness for three dif-- ferent loads

vs.

the angle between the in denter diagonal and the direction [100] .

FiE.2. P/co3/2 ^vs. ^7-oad ^(P) for cracks

a-

long (100) ^and (110). co= radial crack length.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/rphysap:01988002304071900

Microhardness anisotropy in cubic Zro2

HAL Id: jpa-00245874

https://hal.archives-ouvertes.fr/jpa-00245874

Submitted on 1 Jan 1988

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Microhardness anisotropy in cubic Zro2

A. Pajares, F. Guiberteau, A. Dominguez-Rodriguez, A.H. Heuer

To cite this version:

A. Pajares, F. Guiberteau, A. Dominguez-Rodriguez, A.H. Heuer. Microhardness anisotropy in cubic Zro2. Revue de Physique Appliquée, Société française de physique / EDP, 1988, 23 (4), pp.719-719.

�10.1051/rphysap:01988002304071900�. �jpa-00245874�

719

MICROHARDNESS ANISOTROPY IN CUBIC ZrO2

A.PAJARES, F.GUIBERTEAU, A.DOMINGUEZ-RODRIGUEZ and A.H.HEUER.

Departamento de Fisica. F.Ciencias. Univ. Extremadura. 06071 BADAJOZ (SPAIN).

*Departamento de Optica. Facultad de Fisica. Aptdo 1065, 41080 SEVILLA (SPAIN).

**Department of Metallurgy and Materials Science, C.W.R.U., Cleveland, OHIO (U.S.A)

Revue Phys. Appl. 23 (1988) 719 AVRIL 1988,

"he*hardness test is commonly used to determine the low temperature deformation characteristics of brittle compounds. With

this technique, several features can be ob-- tained, mainly the fracture mechanism and

toughness, hardness anisotropy and slip sys

tems.

In this work, the microhardness

(100) planes in Y203-$tabilized cubic Zro2

single crystals has been studied using botn Knoop and Vickers indenters.

The Knoop hardness values(Hk) for dif

ferent loads and orientations

shovin in

fig.l. Crack free endentations are obtained for loads up to 2N and permit determination of the ratio of elastic modulus to hardness

(E/H), as follows /1/:

:b/dis the ratio of the diagonal lengths in

the fully loaded state, which is defined by

the indenter geometry and equal to 7.1; the ratio D’/d’ after unloading is found equal to 8.3. ais

constant equal to 0 45 /1/.

Using this equation

find (E/H)1/2 is in-

dependent of orientation of the indenter di

agonal and equal to 4.7. The Knoop hardness

anisotropy(fig 1) is consistent with either

{100}011&#x3E; or illll110&#x3E; slip systems being

activated under the indenter. A similar

clusion was found in another Ytria - stabi-

lized cubic zirconia /2/.

With

Vickers indent and loads of 2N both radial and lateral cracks

occurs.

The lengths of the radial cracks which

along the indenter diagonals are different

for [100] and [110] directions, being short

er for [100]. The lateral cracks, which

absent when the indenter diagonal is along

[110], allow the stress relaxation and pre- vent the radial cracks from propagating

suggested by /3/.

The fracture toughness(Kc1) can be ob

tained from the len8ht of the radial crack, co, and the value of (E/H)1/2 determined

from the Knoop tests,

follows:

where

xr is

constant equal to 0.016 /4/.

The reaYitionship P/co3/2 is shown in fiG.2

for the two orientations of the indenter di agonal. We find that Kc1 for (100) cracks

is 1.9 MPa ml/2, While Ioci for (110) ones

is 1.1 MPa ml/2.

The lower toughness for (100)compa.red

to (100)planes causes greater stress relief from the elastic / plastic incompatibility

during unloading., such that the incidence of lateral cracking is nearly reduced to ze

ro along [1101. This lower toughness along (110) can be correlated with the fact that the interplanar spacing normal to the (110) planes is larger than that normal to the

(100)planes, but

more microscopic expla-

tion must await future work.

REFERENCES

/1/ D.B.MARSHALL, T.NOMA and A.G.EVANS.

J.Am.Ceram.Soc. 65(1982),C-175.

/2/ J.LANKFORD. J.Mater.Sci. 21(1986),1981

/3/ R.F.COOK and D.H.ROACH. J.Am.Ceram.Soc (to be published).

/4/ C.R.ANSTINS, P.CHANTIKUL, B.R.LAWN and D.B.MARSHALL. J.Am.Ceram.Soc. 64(1981)

Fig.1. Knoop microhardness for three dif-- ferent loads

the angle between the in denter diagonal and the direction [100] .

FiE.2. P/co3/2 vs. 7-oad (P) for cracks

Departamento ^de ^Fisica. F.Ciencias. Univ. Extremadura. 06071 BADAJOZ (SPAIN).

*Departamento ^de Optica. Facultad de Fisica. Aptdo 1065, 41080 SEVILLA (SPAIN).

**Department ^of Metallurgy and Materials Science, C.W.R.U., Cleveland, ^OHIO (U.S.A)

Revue Phys. Appl. ²³ (1988) ⁷¹⁹ ^AVRIL ^1988,

"he*hardness test is commonly ^used ^to determine the low temperature deformation characteristics of brittle compounds. ^With

this technique, several ^features ^can ^{be ob--} tained, mainly ^the ^fracture mechanism and

toughness, ^hardness anisotropy ^and slip _sys

(100) planes ⁱⁿ Y203-$tabilized ^cubic Zro2

single crystals has been studied using ^botn Knoop and Vickers indenters.

The Knoop ^hardness values(Hk) ^for dif

fig.l. ^Crack free endentations are obtained for loads up to 2N and permit determination of the ratio of elastic modulus to hardness

(E/H), ^as ^follows /1/:

:b/dis the ratio of the diagonal lengths ⁱⁿ

the fully ^loaded state, ^{which is} ^defined by

the indenter geometry ând equal ^to 7.1; ^the ratio D’/d’ âfter unloading îs ^found equal to 8.3. ais

constant equal ^to 0 45 ^/1/.

Using ^this equation

^find (E/H)1/2 ^{is in-}

agonal ^and equal to 4.7. The Knoop ^hardness

{100}011> ^or illll110> slip systems being

^occurs.

along the indenter diagonals ^are ^different

for [100] ^and [110] directions, being short

er for [100]. The lateral cracks, ^which

absent when the indenter diagonal ^is along

The fracture toughness(Kc1) ^can ^be ob

tained from the len8ht of the radial crack, co, and the value of (E/H)1/2 ^determined

^follows:

^constant ^equal ^to ^0.016 ^/4/.

for the two orientations of the indenter di agonal. ^We find that Kc1 ^for (100) ^cracks

is 1.9 MPa ml/2, ^While Ioci ^for (110) ^ones

The lower toughness ^for (100)compa.red

to (100)planes ^causes greater stress relief from the elastic / plastic incompatibility

during unloading., such that the incidence of lateral cracking ^is nearly reduced to ze

ro along [1101. This lower toughness along (110) ^can be correlated with the fact that the interplanar spacing normal to the (110) planes ^is larger than that normal to the

(100)planes, ^but

^more microscopic expla-

/3/ R.F.COOK and D.H.ROACH. J.Am.Ceram.Soc (to ^be published).

FiE.2. P/co3/2 ^vs. ^7-oad ^(P) for cracks

long (100) ^and (110). co= radial crack length.